Individual cells display stochastic variability in their responses to activating stimuli. In cells taking part in the innate immune response this variability seems very important. Cells react differently to the same stimulus, e.g. some proliferate some move to apoptosis. Our aim is to develop tools for understanding and accurate modeling of stochastic phenomena in gene transcription and signal transduction in eukaryotic cells. An integral part of the proposal is interdisciplinary training at the undergraduate, graduate and postgraduate level, in which we have experience, involving NSF IGERT grants, Keck Center for Computational Biology and outreach to Texas Medical Center. The primary sources of stochasticity in eukaryotic cells are: (i) Assembly of the transcription complexes attracting RNA Polymerase II. (ii) For low levels of signal, fluctuations in the number of cell membrane receptors binding activating molecule. We are planning to: 1. Identify sources of stochastic effects in gene transcription and regulation on single-cell, nuclear and molecular level and develop mathematical models of these effects. 2. Investigate the mathematical properties of these models by: (a) Finding stochastic solutions, (b) Developing limit theory, (c) Investigating qualitative properties of the models. 3. Develop computational algorithms for model predictions. Implement computer programs for these algorithms. 4. Apply Bayesian and non-Bayesian statistical methodologies for estimating parameters and making inferences about these parameters, and assess the goodness of fit of the models, for inference with complex computer models. The biological system we chose is constituted by 3 pathways involving NFKB family of transcription factors playing a decisive role in innate immunity in mammals. These three are: (i) the canonical, (ii) the RIG-IMAVS-, and (iii) the non-canonical pathways, activated by distinct stimuli, and serve as informative models for computational analysis of stochasticity. We will extend the understanding of these pathways by using fluorescent fusion proteins, analysis of transcription at a single mRNA molecule resolution, chromatin exchange using photobleaching and fluorescence lifetime measurements. In our approach, the biological experiments are motivated by data needed for modeling and estimation, and mathematical methods are based on the observed biological model behavior.